Partial transparency with node editor ignores other objects behind (draws world background)
What I now found out thanks to this video (https://www.youtube.com/watch?v=BKxUKzpx--s), which showed me a slightly different way to get my transparency problem fixed, might be just a solution that was fine for me, because I will stick to game mode anyways.  So others who have the same problem and have no use for 'Blender game' might be dissapointed. It only helps in that direction. (Means, if anyone else has got a concrete solution for nodes editor in blender render, shall feel free to share their knowledge^^)
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After I switched into Blender Game, I went to the materials-tab.  There showed up an option that I desperately needed. It's called "Game Settings" and I just needed to scroll through the options to select 'blend alpha'. This made the texture show up with a blended alpha that worked fine.
When I switched to texture view, the texture still looked wrong; not transparent. I checked the transparency-panel in materials-tab, selected raytrace and set alpha to 0. Now the whole object appeared almost invisible. 
After I then switched to texture-tab and selected full alpha control by the texture, the surface acted like expected. 
Here the screenshots of the told settings:
Materials Tab Texture Tab